Although I agree with Jack Rotman about the damage inflicted by PEMDAS, I'm not sure

. . ."the expression -3^2 deals with the order of operations"

gets to the heart of the problem. The reason is, in this case, the little horizontal bar in front of the 3 could be a part of the number's name. So "-3^2" is not two operations, just like "43^2" is not two operations. In the latter, the 4 is part of the number's name, it is not a multiplier.

This is the problem, in this case, and so I think Guy Brandenburg is right. Writing -3^2 is just asking for trouble.

But, Guy, writing -x^2 is not. This is clearly two operations!

Paul HertzelNIACCMason City, IA

At 11:38 AM 10/18/2012, Jack Rotman wrote:>Phil and all:>>The expression -3^2 deals with the order of >operations; the most advanced operations are >always done first unless a grouping symbol >forces a lower prior operation to be done >first. Since exponentiation is more advanced >than the sign of a number, the exponent only >applies to one symbol (the 3) when there are no grouping symbols.>>Instead of banning this type of problem, I >believe that we should ban PEMDAS or anything >like it. The use of overly simplistic rules >(often stated as a sequence of nouns) >discourages learning and encourages >memorization. If a large rate of correct >answers is the only criteria, just have students >use a calculator and train them on use of >parentheses. If we are teaching mathematics, we >should focus on understanding the priority of >operations. What Phil internalized was this >understanding; saying PEMDAS does not provide >any of the understanding to our students [I >normally spend about a tenth of my time in class >trying to undo the damage of PEMDAS. Undoing >partially correct information is terribly difficult!]>>Even if we never showed -3^2, students would >still be evaluating x^2 for x=-3; knowing that >this means squaring a negative is a part of basic literacy in mathematics.>>For those with an interest, Ive posted some >anti-PEMDAS comments on my blog >(<http://www.devmathrevival.net>www.devmathrevival.net >). You can use the search box on the site to find them.>Jack Rotman>Professor, Mathematics Department>Lansing Community College>(517)483-1079 <mailto:rotmanj@lcc.edu>rotmanj@lcc.edu>www.devmathrevival.net>>From: owner-mathedcc@mathforum.org >[mailto:owner-mathedcc@mathforum.org] On Behalf Of Wayne Ford Mackey>Sent: Thursday, October 18, 2012 12:11 PM>To: Guy Brandenburg; john.peterson20@comcast.net; Philip Mahler>Cc: mathedcc>Subject: RE: Please remind me why -3^2 = -9>>It should be read as the opposite of 3 >squared. Since 3 squared is 9, the opposite is >-9. The "-" sign is used in 3 different >ways. In front of a natural number it means >negative or minus, in front of anything else it >means opposite and between two things it means add the opposite.>>wayne>>>---------->From: owner-mathedcc@mathforum.org >[owner-mathedcc@mathforum.org] on behalf of Guy >Brandenburg [gfbrandenburg@yahoo.com]>Sent: Thursday, October 18, 2012 6:04 AM>To: john.peterson20@comcast.net; Philip Mahler>Cc: mathedcc>Subject: Re: Please remind me why -3^2 = -9>It's a convention. In a case like that, one >really ought to use parentheses to make the >meaning clear, since a lot of people, not just youngsters, will get confused.>>If one intends to say (-3)*(-3), then write >(-3)^2. If one means - (3)*(3), then write - (3^2).>>Writing -3^2 is simply asking for confusion.>>Guy Brandenburg, Washington, DC>http://gfbrandenburg.wordpress.com/>http://home.earthlink.net/~gfbranden/GFB_Home_Page.html>============================>>From: "john.peterson20@comcast.net" <john.peterson20@comcast.net>>To: Philip Mahler <mahlerp@middlesex.mass.edu>>Cc: mathedcc <mathedcc@mathforum.org>>Sent: Thursday, October 18, 2012 6:05 AM>Subject: Re: Please remind me why -3^2 = -9>>Phil,>>-3 means -1 x 3, so -3^2 is (-1)(3^2) = (-1)(9) = -9.>John Peterson>>>---------->From: "Philip Mahler" <mahlerp@middlesex.mass.edu>>To: "mathedcc" <mathedcc@mathforum.org>>Sent: Thursday, October 18, 2012 5:37:07 AM>Subject: Please remind me why -3^2 = -9>>I have been teaching a long time, and I know >from experience that 50% of students will tell >me that 3^2 = +9 on a test or a final, despite >having discussed it a few times in a course.>>When I first started teaching I taught calculus >and precalc. Piece of cake. Then I started with >an Algebra I class and couldnt connect at all >for the first week or so. I was ready to believe >I couldnt teach. I simply could not explain how >I got the right answers when evaluating >expressions... Then I discovered the order of >operations (PEMDAS to some). A definition of the >order of operations which I had so internalized >that I didnt know there was a rule for it. >Since that discovery Ive been a wonderful teacher. :-)>>So... I must be missing something that so many >of my students think 3^2 is +9. What is the rule I have never discovered?>>Full disclosure: I think k^2, k a constant, >should be banned from mathematics texts and >tests. -x^2, x a variable, evaluated for say 3, >absolutely (no pun intended) but not 3^2.>>Phil>